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December 12th, 2009, 06:40 AM   #1
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Ring Homo.



1) show f not a ring homo. over

2) show f is a ring homo. over

for part 2) we have . Then . So we have and . Is this all that has to be shown for 2?

And for part one I dont know how to go about not showing homo.
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December 12th, 2009, 11:55 AM   #2
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Re: Ring Homo.

For part 1, just show any counterexample to f(x + y) = f(x) + f(y) or f(xy) = f(x)f(y). I recommend the additive portion -- every counterexample I can think of for the multiplicative portion exploits the problems of the additive one.
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